So far, the Republican race for the right to challenge President Obama has been a family affair. Republican candidates are talking about Republican issues to woo Republican voters.

But now, Obama’s political machine is pushing its way in to take some shots at Republicans — and having some success.

Just this week, Obama’s team blasted the GOP’s apparent front-runner, Mitt Romney, over his shifting assessments of the president’s economic record.

In Iowa, as former Minnesota governor Tim Pawlenty began a campaign swing Wednesday, he was welcomed with a Democratic Party online video featuring Minnesotans complaining about rising property taxes — with one man saying: “I just don’t understand why this guy thinks he can run for president.”

Obama aides and Democratic officials have fired shots recently at other Republican candidates, as well, including former Utah governor Jon Huntsman Jr. and Rep. Michele Bachmann (R-Minn.).

The exchanges show that Obama and his lieutenants have no intention of sitting quietly by while GOP voters pick their nominee. Democratic officials are reaching into the fray to test out lines of attack against potential 2012 opponents — and maybe make some mischief along the way.

This week, however, Democrats have trained their attention for the most part on Romney. The former Massachusetts governor is trying to solidify his status as the leader in a still-unsettled Republican field. He has maintained his standing in early polls, is assembling a deep organization nationwide and is raising exponentially more money than his opponents. The Romney campaign said Wednesday it had raised $18.25 million over the past three months , while a new outside political action committee run by his allies raised $12 million over the first half of the year.

Some Democrats said they increasingly view Romney as the GOP field’s greatest credible threat should he survive the party primary process.

“He’s the only one who’s plausible,” said Democratic pollster Stanley Greenberg, who has tested public impressions of Romney in recent surveys. “He looks like he could be president. . . . He’s indicated that there’s some path that he could run as a non-extremist presidential candidate.”

A June poll of likely voters by Greenberg’s Democracy Corps group found Romney in a statistical tie with Obama in a hypothetical general election matchup.

Most distressing to Democrats is Romney’s potential appeal to centrist independent voters, a majority of whom swung to Obama in 2008 but who now appear far less smitten.

Unlike many of his rivals, these Democrats say, Romney has presented more centrist views on health care and climate change that could attract swing voters. Greenberg found 42 percent of independents supporting or leaning toward Obama, compared with 44 percent leaning toward or backing Romney.

Another Greenberg survey, a straw poll of liberal activists who attended last month’s Netroots Nation convention, suggested that Romney is viewed in the Democratic base as the greatest threat. A clear plurality — 39 percent of the more than 500 respondents – cited Romney as the candidate they would least like to see win the GOP nomination.

Greenberg and other Democratic strategists said Romney’s history of shifting positions on major issues would probably haunt him through the primaries and would be a major vulnerability if he makes it to the general election.

“That is still hanging around his neck,” Democratic strategist Karen Finney said.

The “flip-flopping” theme was front and center in recent days, as Democrats sought to highlight Romney’s statements about the economy. The dispute began early last week when Democrats attacked Romney for saying that Obama “did not cause this recession, but he made it worse” — despite factual indications that the economy is recovering.

Romney then appeared to step into a trap when he later changed his wording, telling reporters: “I didn’t say things are worse. . . . What I said was the economy hasn’t turned around.”

By this week, Romney was back to his original assertion. “He didn’t make it better,” Romney said at a New Hampshire town hall on Tuesday. “He made things worse.”

Democrats considered this a victory. At a breakfast with reporters Wednesday, David Plouffe, Obama’s top political adviser, described Romney as “a world-class political contortionist.”

Romney aides did not seem the least bit upset about the attacks. In fact, they seemed to relish a confrontation with the president’s team.

“If the Democrats are waiting for Mitt Romney to ease up on his criticism of President Obama’s economic record, it’s simply not going to happen,” Romney spokeswoman Andrea Saul said.

And Romney’s campaign manager took on Plouffe directly and said Romney would debate Obama “any time, any place.”

Democratic officials denied they were singling out Romney for special treatment — insisting they intend to target all of the major GOP contenders.

“I don’t think any of us sit around and say, ‘Well, we’d rather run against this person or that person,’ because they all have flaws that we think we can exploit, not the least of which is their uniform support for the same failed policies that nearly sank our economy,” said Brad Woodhouse, who as communications director at the Democratic National Committee has fired many of the shots at Romney.

The exploitation can go both ways. Last week, when a top Obama aide attacked Bachmann after her official entry into the GOP race, the congresswoman trumpeted it as proof of her potency.

“The president of the United States is threatened by my candidacy,” Bachmann said in an interview with Fox News Channel’s Sean Hannity. “He fears me. He sees me as a serious, substantive competitor.”

In many ways, the Democratic attacks are standard political fare. But such cross-party fire during a primary process can be more Machiavellian than it may appear.

In 2004, for instance, President George W. Bush’s campaign strategists opted not to leave the opposing party’s primary fight solely to chance. As Bush aides would later tell it, they saw the young, charismatic John Edwards as the biggest threat — so they attacked his chief rival for the nomination, John F. Kerry.

“Whomever we attacked was going to be emboldened in Democratic primary voters’ minds,” Bush strategist Matthew Dowd said after the election at a Harvard University forum.

“So we started attacking John Kerry a lot in the end of January because we were very worried about John Edwards,” Dowd said. “And we knew that if we focused on John Kerry, Democratic primary voters would sort of coalesce.”

And veteran Democratic strategist Paul Begala offers a cautionary tale for others in his party who might be gaming out the GOP contest.

“I am haunted and humbled by the legend of Carter supporters saying we want Reagan,” Begala said. “And I think everybody in politics ought to be.”

Staff writer Dan Balz contributed to this report.

More on

Pawlenty adviser apologizes for comment on Bachmann’s ‘sex appeal’

Why Obama won’t ditch Biden for Cuomo in 2012

Romney says Obama made the economy worse